The present invention is generally directed to rotation rate sensors, or gyroscopes, and is specifically concerned with a fiber-optic rotation rate sensor that is particularly suited for use in the mid-course guidance and roll stabilization of missiles.
Gyroscopes have long been in use to detect rotation about an axis. The earliest gyroscopes were of the spinning mass, mechanical variety. While these gyroscopes were generally suitable for use in such applications as course corrections on ships, for example, they are not capable of meeting the dynamic performance requirements associated with mid-course guidance and roll stabilization in missiles, particularly small interceptor missiles. Among the limitations associated with spinning mass gyros are the fact that they have moving parts which can wear out, and they are sensitive to the forces of gravity, shock and vibration. Furthermore, a missile might experience temperature variations in the range of -65.degree. C. to 85.degree. C., either in storage or while in use, and the mechanical gyros do not operate readily over such a wide range. In addition, their response time is severely limited.
A second type of gyroscope is an optical version that is commonly known as a ring laser gyro. While offering advantages over the mechanical type of gyroscope, the ring laser gyro is also not without its attendant limitations that restrict its suitability for use in such applications as missile guidance and stabilization. Included in such limitations are the complexity of its construction, relatively large size, alignment considerations, high voltage requirements, gas sealing problems, and the need for mechanical dithering to prevent lock in.
Furthermore, a missile can lay dormant in a silo or other storage facility for a considerable period of time, e.g., up to 10 years, before it is put to use and the gyroscope is required to function. Neither spinning mass nor ring laser gyroscopes have proven to be dependable under such long dormancy conditions.
A third type of gyroscope, and the one which is most practically suited for use in missile guidance types of applications, is the fiber-optic gyroscope. This type of gyroscope operates in accordance with the principle known as the Sagnac effect. Basically, this principal states that when two beams of light travel in opposite directions around an enclosed area such as a loop, any rotation of the loop about its axis will produce a relative phase difference between the two beams, and the magnitude of this phase difference will be proportional to the rate of angular rotation about the loop axis. In implementing the Sagnac effect, a fiber-optic gyroscope employs an optical fiber loop whose axis is parallel to the axis about which rotation is to be measured. Two light beams are fed into the respective ends of the loop, and any relative phase shift between them is detected by measuring the interference of the beams on a detector.
The intensity of the measured interference pattern is given by the equation: EQU I=I.sub.0 (1-cos K.OMEGA.) (1)
where I.sub.0 is a peak, or initial beam intensity, K is the Sagnac scale factor and .OMEGA. is the rate of angular rotation. The Sagnac scale factor K is defined as: ##EQU1## where N is the number of times each beam travels around the loop area A normal to the axis of rotation, c is the speed of light and .lambda. is the wavelength of the light in the beam. For a fiber optic coil, N can be made quite large so that the area A can be small while maintaining high sensitivity.
When measuring relatively small rates of angular rotation, the sensitivity of the fiber-optic gyroscope is low if the cosine dependent measurement of Equation (1) is utilized. More particularly, at a zero input rate, the slope of the cosine function is zero and it varies only slightly with small changes around zero. In addition, the cosine function is symmetric about the zero axis, so that the magnitude of the intensity measured according to equation (1) is independent of the direction of rotation. To compensate for this situation and to achieve greater sensitivity of the measurement around a zero input rate, two approaches have been utilized. One is to the shift the phase of one beam 90.degree. relative to the other, so that the output signal is sine-dependent rather than cosine-dependent. The other approach is to shift the frequency of one beam relative to the other.
The present invention is concerned with this latter approach, and is particularly directed to output phase errors that can arise in a practical implementation of this approach. More particularly, when modulation is applied which shifts the frequency of one light beam relative to the other, the output phases, .phi..sub.1 and .phi..sub.2 of the two beams are respectively given by: ##EQU2## where .omega..sub.1, .omega..sub.2, are the respective angular frequencies of the light, n.sub.1, n.sub.2 is the refractive index of the fiber, accounting for dispersion, l is the length of the fiber, and t.sub.1 and t.sub.2 are defined as t.sub.1 =t+.DELTA.t and t.sub.2 =t-.DELTA.t where t is the nominal time it takes the beam to traverse the loop and .DELTA.t is the time delay introduced by the Sagnac Effect. If it is assumed that small modulation frequencies are used and hence n.sub.1 .perspectiveto.n.sub.2 =n, the output phase difference between the two beams after propogating through the loop is given by: ##EQU3##
The last term appearing in this expression will be recognized as the Sagnac effect phase shift. The first term defines an added phase offset that is due to the phase modulation, i.e., .omega..sub.1 .noteq..omega..sub.2. Accordingly, the output signal from the fiber optic gyro is subject to variations in fiber length, fiber index of refraction and modulation. This term can be significant because of the sensitivity of fiber length and index of refraction to temperature and stress. Attempts at using a non-fiber optical reference channel do not compensate for this term. Although the non-fiber optical reference channel may compensate for phase errors occuring within the modulator, because it is optically different from the fiber optic channel it will generally not behave the same.